Weak value expansion of quantum operators and its application in stochastic matrices

2013/06/20 by Taksu Cheon, Cheon, Taksu, Sergey S. Poghosyan +2
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1306.4767

8 pages ReVTeX with 4 eps figures

arxiv created 2013/06/20 · openalex publication_date 2013/06/20 · arxiv updated 2013/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that any Hermitian operator can be expanded in terms of a set of operators formed from biorthogonal basis, and the expansion coefficients are given as products of weight functions and weak values, shedding a new light on the physical interpretation of the weak value. The utility of our approach is showcased with examples of spin one-half and spin one systems, where irreversible subset of stochastic matrices describing projective measurement on a mixed state is identified.

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